What is the Least Common Multiple of 78015 and 78030?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 78015 and 78030 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78015 and 78030, than apply into the LCM equation.

GCF(78015,78030) = 15
LCM(78015,78030) = ( 78015 × 78030) / 15
LCM(78015,78030) = 6087510450 / 15
LCM(78015,78030) = 405834030

Least Common Multiple (LCM) of 78015 and 78030 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78015 and 78030. First we will calculate the prime factors of 78015 and 78030.

Prime Factorization of 78015

Prime Factorization of 78030

Now multiplying the highest exponent prime factors to calculate the LCM of 78015 and 78030.

LCM(78015,78030) = 3³ × 5¹ × 7¹ × 743¹ × 2¹ × 17²
LCM(78015,78030) = 405834030